   Chapter 10.1, Problem 35E

Chapter
Section
Textbook Problem

# Sketching a Hyperbola In Exercises 37-40, find the center, foci, vertices, and eccentricity of the hyperbola, and sketch its graph using asymptotes as an aid. x 2 25 − y 2 16 = 1

To determine
The centre, foci, vertices and eccentricity of the provided hyperbola also draw the graph with asymptotes as an aid.

Explanation

Given: The equation of hyperbola, x225y216=1.

Explanation:

Consider the standard equation of hyperbola, (xh)2a2(yk)2b2=1

Where a represents the transverse axis and b represents the conjugate axis. The ordered pair (h, k) is the centre of the hyperbola.

Thus, for the provided hyperbola, the centre is (0, 0) and the values of a and b are 5 and 4 respectively.

Hence, the vertices are (5, 0) and (-5, 0)

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